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NCD

Soldering will INCREASE the likelihood of lead-in tinsel wire failure.

Damaging the lead-in wires like that is always a sign of gross overpowering at low frequencies.
It seemed like they were soldered to begin with. They poke into the back hole of the pin plate, and look like they're attached right there with the pins. Is that not correct?
 
My engineering partner of 30+ years worked on the vibrational destructive testing program for the Apollo re-entry vehicle. They routinely shredded seemingly strong assemblies.
With appropriate instrumentation/sensors looking the right parameters you can see and/or calculate the changes that are an early indication of a part headed for failure. It is amazing how frequently a part that is fatigued but not yet failed will create a load/excitation path or stress that actually leads another part to fail first.

The real surprise though is just what you mentioned in that seemingly indestructible parts can be brought to the end of their operational life faster than anyone thought possible. The other thing is that many parts have multiple potential failure modes including for example high and low cycle fatigue.

So bore-sighting on only what you assume is the most important concern as a leading/key indicator to stay safe can have you inadvertently missing other stressing conditions that might arise with a different operational use case. Aircraft frequently experience this related to how the aircraft is flown (stressed) based on the types of missions they are used for. Commercial aircraft even see some levels of variation with short and long haul routes and different types of airport associated characteristics that can be more stressing on planes and pilots.
 
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Depends on the specific terminal board, but most drivers are no longer built this way because when they are driven very hard (usually beyond their rated mechanical power handling), that joint will fatigue-fail IF the solder extends past the edge of the hole.

Most manufacturers of higher powered speakers no longer do this, they bring the tinsel lead through the hole, make a 90 degree turn and crimp or solder above. They then fill the hole with a rubberized PVA adhesive. Other manufacturers use an inverted terminal on the back and roll the tinsel into the lead before soldering and often will use a short piece silicone at the joint to minimize the potential for fatigue stress fracture. There's a lot of engineering that goes into mechanical robustness of high powered speakers.
 
Depends on the specific terminal board, but most drivers are no longer built this way because when they are driven very hard (usually beyond their rated mechanical power handling), that joint will fatigue-fail IF the solder extends past the edge of the hole.

Most manufacturers of higher powered speakers no longer do this, they bring the tinsel lead through the hole, make a 90 degree turn and crimp or solder above. They then fill the hole with a rubberized PVA adhesive. Other manufacturers use an inverted terminal on the back and roll the tinsel into the lead before soldering and often will use a short piece silicone at the joint to minimize the potential for fatigue stress fracture. There's a lot of engineering that goes into mechanical robustness of high powered speakers.
Hmm alright. Now I wish I would've took a picture. I just replaced the screw I stripped out yesterday, I could've just pulled it again and snapped a pic.

So the copper wires go through the hole. No silicone or anything, but also no visible solder from the back side. The only solder is pinning the terminals on the other side. My intuition told me that the wire makes contact from the bottom, and it's all pinned together at that point. I held the wire in the hole, and soldered it to the casing. Boom, worked. Seems solid too. But, maybe I should just order another speaker to have on standby anyway. Right?

Maybe PVA the rest of them while I'm at it.
 
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Just don't do that again and the speakers will be fine.
Hahaha. I do it with everything horse. Don't know limits until you push limits. This is the first time something broke with no mechanical scream first. Usually, there's a big, "Ouch! Don't do that!" And I find out where that point is. This one, stayed clean and clear all the way through the snap.